No blockchains are anywhere close to "untenably huge".
The ethereum chain is 639.43 GB.
A $10 USD VPS could sync with that in under two hours. That is about $12 USD of hard drive space after 5 years.
This is about the same as downloading the five to eight largest games on steam.
> and ethereum fees are often higher than Bitcoin fees.
No they aren't. They are about the same, making them both unusable for normal transactions, but it should be obvious there are no technical limitations to making larger and/or more frequent blocks since ethereum does it already.
https://bitinfocharts.com/comparison/transactionfees-btc-eth...
> It doesn't have to be "synced with the chain" except during channel opening and closing, which occur infrequently (like on the scale of weeks or months).
Which means that no one can use that balance for weeks or months and some third party has to spot people the money in the mean time. That sounds like a credit card. Know what doesn't work like that? On chain transactions.